CN108445765B - Calibration method for airplane automatic drilling and riveting parallel posture adjusting bracket - Google Patents
Calibration method for airplane automatic drilling and riveting parallel posture adjusting bracket Download PDFInfo
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Abstract
A calibration method of an airplane automatic drilling and riveting parallel posture adjusting bracket can be used for calibration of industrial parallel robots. Aiming at the target pose, solving the ideal displacement of each active moving pair by adopting inverse kinematics solution under the nominal structure parameters; driving the active moving pair to move according to the calculated ideal displacement of each active moving pair; after the movement is stopped, measuring the coordinates of the appointed point on the bracket by using a laser tracker, and fitting the actual pose of the bracket; comparing the actual pose of the bracket with the target pose to determine the pose error of the bracket before calibration; establishing an error model between a bracket pose error and a structural error and between active moving pair displacement quantities by adopting a space vector chain method, and identifying the structural error by adopting a least square method; and correcting the nominal structure parameters of the bracket, performing inverse kinematics solution again, and determining the displacement of each active moving pair when the target pose is to be reached. The method is simple, the identification precision is high, the motion precision of the bracket is improved, and the requirement of the bracket posture adjustment precision can be met to the maximum extent.
Description
Technical Field
The invention relates to a mechanical positioning method, in particular to a technology for positioning a drilling and riveting head on a complex surface, and specifically relates to a method for calibrating an automatic drilling and riveting parallel attitude-adjusting bracket of an airplane based on a positioner.
Background
The aircraft has large area of parts, difficult processing, low efficiency by adopting a manual assembly mode, difficult guarantee of precision and great influence on the service life and the safety factor of the aircraft. In order to solve the above problems, various countries around the world use automated assembly techniques for assembling large aircraft components such as aircraft panels and various types of automated assembly systems have been designed.
Nanjing aerospace university has designed planer-type automatic drilling and riveting system according to the work piece processing requirement, disposes the parallelly connected appearance bracket of transferring of novel locator class that has adjustment gesture and position function for the automatic operation of riveting of boring of aircraft: the gantry system is designed with x, y and z-direction movement freedom degrees and rotation freedom degrees around an x axis, the movement precision of the rotation axis around the x axis is low, and in order to ensure the rotation precision of the automatic drilling and riveting system around the x axis, the bracket is designed with the rotation freedom degrees around the x axis; the gantry system is not designed with the rotational freedom degree around the y axis, and in order to realize the posture adjustment around the y axis, the bracket system is designed with the rotational freedom degree around the y axis; in order to realize the freedom of rotation of the bracket around the x axis and the y axis, each positioner is designed with the freedom of movement in the z direction. The parallel posture-adjusting bracket consists of four positioners (as shown in figure 2): the 1 st positioner is only provided with a z-direction active moving pair, the 2 nd positioner is provided with an x-direction active moving pair and a z-direction active moving pair, the 3 rd positioner and the 4 th positioner are provided with x-direction, y-direction and z-direction moving pairs, wherein the z-direction is the active moving pair, and the x-direction and the y-direction are follow-up moving pairs; each locator and the bracket are connected through a spherical hinge pair SiConnecting; the structure of the bracket posture adjusting system is shown in figure 3, Xi、Yi、ZiThe slide pair is shown, i is 1,2,3,4, and the positioner number is shown. In the using process of the bracket, the problem of inaccurate posture adjustment exists, in order to solve the problem, calibration is needed, the calibration schematic diagram is shown in figure 1, and Om-XmYmZmFor the laser tracker coordinate system, Ob-XbYbZbAs a global coordinate system of the gantry, Ot-XtYtZtA local coordinate system of the carriage.
Many scholars have conducted a great deal of research on reducing attitude errors of the whole parallel mechanism, but the research on the attitude errors and the structural errors of the parallel mechanism of the positioner is less. The existing research on the parallel posture-adjusting bracket of the positioner has the following defects: 1) all constraint equations are not brought into an error model, so that the established error model cannot identify the angle error of the active moving pair of the single main drive positioner, and for the parallel posture adjusting bracket, if the existing mode is adopted for modeling, most of the angle errors of the active moving pair cannot be identified by the error model; 2) the structural error item coefficient matrix identification structural error is formed by multiplying the transposition of the matrix by the original matrix, the error item coefficient matrix is a singular matrix, matrix singularity is eliminated by a regularization method, the error item coefficient is caused to change, and the structural error identification accuracy is reduced.
Disclosure of Invention
The invention aims to provide a method for calibrating an automatic drilling and riveting parallel attitude-adjusting bracket of an airplane based on a positioner, aiming at the problem that the existing bracket is low in attitude-adjusting and positioning precision.
The technical scheme of the invention is as follows:
a calibration method of an automatic drilling and riveting parallel attitude-adjusting bracket of an airplane is characterized in that aiming at a target attitude, the ideal displacement of each active moving pair is solved by inverse kinematics under nominal structure parameters; driving the active moving pair to move according to the calculated ideal displacement of each active moving pair; after the movement is stopped, measuring the coordinates of the appointed point on the bracket by using a laser tracker, and fitting the actual pose of the bracket; comparing the actual pose of the bracket with the target pose to determine the pose error of the bracket before calibration; establishing an error model between a bracket pose error and a structural error and between active moving pair displacement quantities by adopting a space vector chain method, and identifying the structural error by adopting a least square method; and correcting the nominal structure parameters of the bracket, performing inverse kinematics solution again, and determining the displacement of each active moving pair when the target pose is to be reached.
The method comprises the following specific steps:
(1) before calibration, a laser tracker is adopted to measure coordinates of designated points on the bracket, an actual pose A of the bracket is fitted, and for a target pose B, inverse kinematics solution is adopted under nominal structure parameters to calculate the ideal displacement of each active moving pair from the pose A to the pose B;
(2) driving the active kinematic pair to move according to the calculated ideal motion amount of each active kinematic pair, and measuring the coordinates of a specified point on the bracket by using a laser tracker to fit an actual pose C of the bracket;
(3) comparing the actual pose C of the bracket with the target pose B, and determining the pose error of the bracket before calibration;
(4) establishing an error model between a bracket pose error and a structural error and between active moving pair displacement quantities by adopting a space vector chain method, and identifying the structural error by adopting a least square method;
(5) and correcting the nominal structure parameters of the bracket, performing inverse kinematics solution again, and determining the displacement of each active moving pair when the target pose B is to be reached.
The invention has the beneficial effects that:
the error model suitable for the novel automatic drilling and riveting parallel posture adjusting bracket is established, all constraint equations are brought into the error model, the error identification precision is improved, and the angle error of the active moving pair of the single main-driven positioner can be identified; meanwhile, the structural error is identified by adopting a matrix dimension reduction mode, and the error identification precision is ensured on the premise of not changing the structural error item coefficient.
The established error model is combined with auxiliary measurement, so that the calibration of the parallel posture-adjusting bracket is realized: the error identification result shows that the identification precision of the invention is superior to the existing identification method; the error compensation result shows that the motion precision of the bracket is obviously improved, and the requirement of airplane assembly on the posture adjusting precision of the bracket can be met.
Drawings
Fig. 1 is a schematic diagram of laser tracker calibration.
Fig. 2 is a schematic view of the positioner.
Fig. 3 is a schematic view of the bracket structure.
Fig. 4 is a schematic view of a carriage vector chain.
Fig. 5 is a detailed view of the carrier vector chain.
FIG. 6 is a diagram illustrating the recognition accuracy of the present invention.
FIG. 7 is a diagram illustrating the recognition accuracy of the prior recognition method.
Detailed Description
The invention is further described with reference to the following figures and detailed description.
As shown in fig. 1-7.
A calibration method for an automatic drilling and riveting parallel attitude-adjusting bracket of an airplane comprises the following specific steps:
(1) before calibration, a laser tracker is adopted to measure coordinates of designated points on the bracket, an actual pose A of the bracket is fitted, and for a target pose B, inverse kinematics solution is adopted under nominal structure parameters to calculate the ideal displacement of each active moving pair from the pose A to the pose B;
(2) driving the active kinematic pair to move according to the calculated ideal motion amount of each active kinematic pair, and measuring the coordinates of a specified point on the bracket by using a laser tracker to fit an actual pose C of the bracket;
(3) comparing the actual pose C of the bracket with the target pose B, and determining the pose error of the bracket before calibration;
(4) establishing an error model between a bracket pose error and a structural error and between active moving pair displacement quantities by adopting a space vector chain method, and identifying the structural error by adopting a least square method;
(5) and correcting the nominal structure parameters of the bracket, performing inverse kinematics solution again, and determining the displacement of each active moving pair when the target pose B is to be reached.
The details are as follows:
when the bracket kinematics is reversely solved, the original points of the reference coordinate systems of the positioners 1 to 4 are respectively positioned at X1＝0、X2＝0、X3＝0、X4At 0, i.e. O1、O2、O3、O4At a point, the orientation transformation matrix of the localizers 1 to 4 with respect to the base coordinate system is set to "diag (1,1, 1"). Origin of the base coordinate system is ObThe X-axis direction of the point-base coordinate system is parallel to the ideal sliding pair X4From S2Point to S1The Y axis of the base coordinate system is parallel to the ideal sliding pair Y4From S1Point to S4The base coordinate system has a Z-axis parallel to the ideal sliding pair Z4In the direction of ObPoint to S1. The vector of the center point of the bracket relative to the origin of the base coordinate system is P, and the vector of the center of the spherical hinge relative to the origin of the reference coordinate system of the bracket is P
The vector of the origin of the reference coordinate system of the locator relative to the origin of the base coordinate system is lambdai；S1、S2、S3、S4The centers of the spherical hinges corresponding to the positioners 1-4 are respectively; siAnd OiEach moving pair of the positioner is included between the two moving pairs, i is 1,2,3 and 4 and is the serial number of the positioner; o isbAnd O1And (4) overlapping.
Defining: (1) the position error is derived from the 21 item geometric error and is the difference between the actual movement distance and the target movement distance when the kinematic pair moves; (2) "position error" is the error of the point relative to the coordinate system in x, y, z directions, such as the position error of the center point of the spherical hinge relative to the origin of the coordinate system of the bracket, the position error of the center point of the bracket relative to the base coordinate system; (3) the 'active kinematic pair angle error' refers to an angle error between an actual direction vector and an ideal direction vector of an active kinematic pair.
Each positioner corresponds to a moving branched chain, taking the branched chain 3 as an example, a closed-loop space vector chain related to a base coordinate system, a positioner reference coordinate system, a spherical hinge center and a bracket coordinate system is established, the bracket vector chain is established in a manner shown in fig. 4 and 5, and the closed-loop space vector chain establishment methods corresponding to the positioners 1,2 and 4 are similar.
Center point S of spherical hingeiRelative to the origin O of the base coordinate systembThe vector of (a) is:
SiOb＝E·(li1·ei1+li2·ei2+li3·ei3)+λi (1)
assuming that the bracket posture adjusting mechanism is in a certain posture in a working space, the posture adjusting mechanism can be obtained by using a space vector chain method:
wherein e isi1＝(1,0,0)T，ei3＝(0,0,1)T，ei3＝(0,0,1)TRespectively representing x, y and z direction unit vectors of the ith positioner, wherein i represents a positioner number; assuming bracket center point OtThe coordinate is (x)p,yp,zp)TThen the center point O of the brackettRelative to the origin O of the base coordinate systembIs (x)p,yp,zp)T；
Is the attitude transformation matrix of the bracket coordinate system relative to the base coordinate system, c represents cos, is s represents sin:
wherein, alpha is a bracket pivoting shaft OtXtAngle of rotation, beta being the axis O of the carriertYtAngle of rotation, gamma being the axis O of the carriertZtThe positive and negative of alpha, beta and gamma satisfy the right-hand rule; li1、li2、li3The motion amounts of the ith positioner in the x, y and z directions are respectively represented, and if i is 1,2,3 and 4, the driving amount of each active moving pair in the target pose is the ideal inverse solution model, which can be represented as follows:
wherein the content of the first and second substances,
the secondary initial height is actively moved in the z direction.
And (3) establishing a relational equation of bracket pose errors, ideal active moving pair driving quantity, structural errors and nominal structural parameters by taking the branched chain 1 as an analysis object: the branched chain 1 is a single driving branched chain, the driving direction is the z direction, and according to the space vector chain principle:
the differential is obtained at both ends of equation (5):
wherein, δ e13Represents the z-direction active movement pair angular error of the positioner 1:
wherein the content of the first and second substances,
the differential operator is obtained by subtracting a unit matrix from a differential rotation matrix; delta theta13x、δθ13y、δθ13zRespectively representing the angle error and the radian value of the active moving pair of the positioner 1 in the z direction and ideal x, y and z axes. δ P represents a position error of the center point of the carriage with respect to the base coordinate system, δ P ═ δ xp,δyp,δzp)T；
Represents the differential of the rotation matrix of the gantry coordinate system with respect to the base coordinate system:
wherein, δ α, δ β, δ γ respectively represent attitude error, camber value of the bracket coordinate system relative to the base coordinate system; delta l13Represents the z-direction position error, δ l, of the positioner 121、δl23、δl33、δl43The definitions are similar;
indicating the position error of the center of the corresponding spherical hinge of the positioner i relative to the origin of the bracket coordinate system,
δλirepresents the error of the initial position of the origin of the base coordinate system of the positioner relative to the position of the origin of the base coordinate system, delta lambdai＝(δλix,δλiy,δλiz)T；i＝1,2,3,4。
The establishment mode of the constraint equation corresponding to the branched chain 2 is the same as that of the branched chain 1; the branched chains 3 and 4 are single driving branched chains, the main driving direction is the z direction, the x direction and the y direction follow up, and according to the space vector chain principle:
differentiating the two ends of equation (7) yields:
wherein, δ li1、δli2The position error of the follow-up moving pair is obtained; delta ei1、δei2The angle error of the servo moving pair is obtained; regardless of the servo moving pair position degree error and the servo moving pair angle error, the formula (8) can be simplified as follows:
wherein, i is the locator number, i is 3, 4; the remaining variables in equation (9) are defined as above.
The equation obtained after the vector chain corresponding to each branched chain is differentiated (for example, the equation (6) corresponding to the branched chain 1) comprises three constraint equations, all the constraint equations of each branched chain are put into an error model, and then vectors are multiplied on two sides of the equation obtained after the vector chain is differentiated in sequence
The constraint equations are separated. Vector is multiplied by both sides of equation (6)
For example, the following steps are carried out:
wherein:
δe21、δe23、δe33、δe43the linearization pattern is similar. Using 0 for 1 × 1 order matrix and 0 for 1 × 3 order matrix, the following equation can be obtained after sorting:
Tl·δl+Te·δe-Tλ·δλ＝Tpθ·δpθ (10)
wherein the content of the first and second substances,
wherein the content of the first and second substances,
Tlis a 12 × 5 order matrix, deltalIs a 5 × 1 order matrix, TeIs a 12 × 15 order matrix, deltaeIs a 15 × 1 order matrix, TλIs a 12 × 21 order matrix, deltaλIs a 21 x 1 order matrix, TpθIs a 12 × 6 order matrix, deltapθIs a 6 x 1 order matrix. The formula (10) is arranged to obtain:
wherein [ Tl Te -Tλ]Is a 12 × 41 order matrix, [ delta ]l δe δλ]TIs a 41 x 1 order matrix. Equation (11) can be simplified as:
Ti·δ＝(Tpθ·δpθ)i (12)
due to delta e13、δe21、δe23、δe33、δe43Each containing two unknowns, so equation (12) contains 41-5-36 unknowns, and a single pose can provide 12 algebraic equations about the unknowns, so to identify all 36 pose errors, 3 or more sets of pose error data need to be measured to form an overall error model in the case that the row vectors and the column vectors of the matrix T are linearly independent:
wherein n is the number of pose groups, formula (13) can be abbreviated as:
T·δ＝M (14)
however, the T matrix in the formula (14) includes a plurality of 0 vector columns, has a large condition number, is sensitive to measurement errors, and is poor in identification effect when the T matrix in the formula (14) is directly used for identifying structural errors, so that structural error identification analysis is required to be performed, and dimension reduction processing is performed on the T matrix.
When the structural error is identified, the structural error item with the coefficient being zero has no influence on the pose of the bracket, and the linearly related structural error needs to be identified integrally, so that the dimension reduction processing needs to be carried out on the coefficient matrix, and x is used for carrying out dimension reduction processing1、x2…x36Respectively corresponding to the structural error term δ l13、δl21…δλ4zThe correspondence between x and the error term is shown in table 1.
TABLE 1 correspondence of x terms to error terms
As can be seen from equation (14):
1) the 8 th, 9 th, 14 th, 17 th and 20 th columns of the matrix T are vector columns 0 and the corresponding unknowns are 0, so that the relevant columns can be directly eliminated from the coefficient matrix T to form a matrix T'. The indirect solution of the corresponding structural errors of the 8 th column, the 14 th column, the 17 th column and the 20 th column in the matrix T can be carried out through the actual measurement, namely the laser tracker measurement bracket only moves and adjusts the position change of the designated point of each locator sliding pair in the process of the gesture movement in the z direction; the structure error corresponding to the 9 th column in the matrix T can be wound by the bracket S1S4The change in the spatial position of a specified point on the x-axis of movement of the measurement locator 2 is calculated indirectly by rotation.
2) Since the matrix T' is linearly related in the 2 nd and 22 nd columns, linearly related in the 3 rd and 24 th columns, linearly related in the 4 th and 30 th columns, and linearly related in the 5 th and 36 th columns, without loss of generality, taking the 2 nd and 22 nd columns as an example in any row, then:
1×(x2+x22)+f(x1,x3…x36)＝Δii
wherein, DeltaiiMultiplying the integral error term coefficient in the process of adjusting the posture of the bracket at a time by an error term (namely (T)pθ·δpθ)iMiddle row), f (x)1,x3…x36) To remove structural errors x2、x22Then, the remaining structural error pairs ΔiiThe influence of (c). The structural error items corresponding to the linear correlation rows cannot be identified independently, and only the comprehensive influence of the structural error items on the integral error items of the bracket can be identified. Similarly, the following terms in equation (18) can be solved as a single whole: x is the number of3+x24；x4+x30；x5+x36. Therefore, let:
Q2＝x2+x22；Q3＝x3+x24；Q4＝x4+x30；Q5＝x5+x36
the corresponding coefficient matrix T 'is arranged to obtain an error transformation matrix T' with the row number of 32, so that the structural error parameters needing to be identified are transformed into x1、Q2、Q3、Q4、Q5、x6、x7、x8、x9、x10、x11、x12、x13、x14、x15、x16、x17、x18、x19、x20、x21、x23、x25、x26、x27、x28、x29、x31、x32、x33、x34、x35Then equation (14) can be modified as:
T″·δ＝M (15)
the T matrix in the formula (14) is subjected to dimensionality reduction, and the condition number of the matrix T is changed from 1021Reduced to 103And (4) reducing the sensitivity of the matrix T to measurement errors. The error terms in the formula (15) obtained by dimension reduction can be completely identified, the matrix T 'can be divided by the matrix M in the matlab, or the matrix T' is multiplied by the two sides of the formula (15)TAfter the coefficient matrix is changed into a nonsingular matrix, the inverse solution delta is obtained, and x is known from the section 1) of the section2、x3、x4、x5Can be measured and indirectly calculated, then x22、x24、x30、x36The method can be used for solving the problems. So far, all the structural errors of the parallel posture-adjusting bracket can be identifiedAnd (4) poor.
Errors that can only be identified by the error model:
only errors identified can be measured: delta l21、δl23、δl33、δl43(ii) a The error term can be calculated only indirectly: delta lambda2x、δλ2z、δλ3z、δλ4z(ii) a Errors identifiable by error model and measurement: delta l13、δθ13y、δθ13x、δθ21z、δθ21y、δθ23y、δθ23x、δθ33y、δθ33x、δθ43y、δθ43x。
Compared with a modeling mode of incorporating all constraint equations into an error model, the modeling mode of not incorporating all constraint equations into the error model has low structural error identification precision. A group of structure errors are randomly given, and an error item with larger difference between the given value and the identification value is selected for analysis, so that the maximum value of the difference between the structure errors identified by the method and the given value is 0.1mm, which is superior to the maximum value of the difference between the structure errors identified by the existing identification method and the given value, which is 1.13mm, as shown in fig. 6 and 7.
Correcting the actual structure parameters of the attitude adjusting mechanism, performing inverse kinematics solution again on the basis of the corrected structure parameters aiming at the target pose, inputting the structure errors identified by the target pose, the nominal structure parameters and the error model into an equation set (16), outputting the structure errors identified by the error model into the motion amount of each axis after correction, and calculating and considering the structure errors deltaerror2The driving amount of each active sliding pair and the amount of each follow-up sliding pair are determined.
Wherein i is the locator number; li3aIndicates the actual driving amount, l, of the active z-direction moving pair of the positioner i21aRepresents the x-direction actual driving amount of the positioner 2; e.g. of the typei3aRepresenting the z-direction active shift pair actual direction vector of the ith positioner; e.g. of the type21aRepresents the x-direction active shift pair actual direction vector of the positioner 2;
representing the actual vector of the central point of the spherical hinge relative to the origin of the bracket coordinate system; lambda [ alpha ]iaRepresenting the actual vector of the origin of the coordinate system of the positioner relative to the origin of the base coordinate system; i is 1,2,3, 4.
In order to solve the compensated bracket pose error, an equation set (17) corrects elements related to the structural error on the basis of an ideal forward solution vector chain (2) of each branched chain, inputs motion quantity and actual structural parameters of each axis solved for inverse solution of the corrected kinematics, and outputs the motion quantity and the actual structural parameters of each axis as the calibrated actual pose P theta of the mechanism2And ideal pose P theta0Compared with the prior art, the calibrated pose error is greatly reduced, and the requirement on operation precision is met.
The present invention is not concerned with parts which are the same as or can be implemented using prior art techniques.
Claims (1)
1. A calibration method of an automatic drilling and riveting parallel attitude-adjusting bracket of an airplane is characterized in that for a target attitude, the ideal displacement of each active moving pair is solved by inverse kinematics under nominal structure parameters; driving the active moving pair to move according to the calculated ideal displacement of each active moving pair; after the movement is stopped, measuring the coordinates of the appointed point on the bracket by using a laser tracker, and fitting the actual pose of the bracket; comparing the actual pose of the bracket with the target pose to determine the pose error of the bracket before calibration; establishing an error model between a bracket pose error and a structural error and between active moving pair displacement quantities by adopting a space vector chain method, and identifying the structural error by adopting a least square method; correcting the nominal structure parameters of the bracket, performing inverse kinematics again, and determining the displacement of each active moving pair when the target pose is to be reached; during error modeling, constraint equations in all directions are separated one by one, all the constraint equations are incorporated into an error model, error identification precision is improved, and the angle error of the active moving pair of the single main driving positioner can be identified; during error identification, an error coefficient matrix is optimized by combining auxiliary measurement, a structural error is identified by adopting a matrix dimension reduction mode, and the error identification precision is ensured on the premise of not changing a structural error item coefficient; the error modeling is specifically as follows: equation of
Tl·δl+Te·δe-Tλ·δλ＝Tpθ·δpθ
Wherein the content of the first and second substances,
wherein e isi1＝ex＝(1,0,0)T，ei2＝ey＝(0,0,1)T，ei3＝ez＝(0,0,1)TRespectively representing x, y and z direction unit vectors of the ith positioner, wherein i represents a positioner number; li1、li2、li3Respectively represent the ith positioningThe amount of movement of the device in the x, y and z directions;
is a posture transformation matrix of the bracket coordinate system relative to the base coordinate system;
representing a differential of the rotation matrix of the gantry coordinate system with respect to the base coordinate system;
representing the position error of the center of the spherical hinge corresponding to the positioner i relative to the origin of the bracket coordinate system; delta lambdaiRepresenting the error of the initial position of the origin of the base coordinate system of the positioner relative to the position of the origin of the base coordinate system; delta li1、δli2、δli3The position error of the follow-up moving pair is obtained; delta ei1、δei2、δei3The angle error of the servo moving pair is obtained; the vector of the center of the spherical hinge relative to the origin of the reference coordinate system of the bracket is
The vector of the origin of the reference coordinate system of the locator relative to the origin of the base coordinate system is lambdai；
TlIs a 12 × 5 order matrix, deltalIs a 5 × 1 order matrix, TeIs a 12 × 15 order matrix, deltaeIs a 15 × 1 order matrix, TλIs a 12 × 21 order matrix, deltaλIs a 21 x 1 order matrix, TpθIs a 12 × 6 order matrix, deltapθIs a 6 multiplied by 1 order matrix; finishing the formula to obtain:
wherein [ Tl Te -Tλ]Is a 12 × 41 order matrix, [ delta ]l δe δλ]TIs a 41 × 1 order matrix; the above formula is simplified as follows:
Ti·δ＝(Tpθ·δpθ)i
due to delta e13、δe21、δe23、δe33、δe43Each containing two unknowns, so the above equation contains 41-5 ═ 36 unknowns, and a single pose can provide 12 algebraic equations about the unknowns, so to identify all 36 pose errors, 3 or more sets of pose error data need to be measured to form an overall error model in the case that the matrix T row vectors and column vectors are linearly independent:
wherein n is the number of pose groups, the above formula is abbreviated as:
T·δ＝M
the specific way of the matrix optimization is as follows: 1) the 8 th column, the 9 th column, the 14 th column, the 17 th column and the 20 th column of the matrix T are zero vector columns, and corresponding unknowns are 0, so related columns are directly removed from the coefficient matrix T to form a matrix T'; indirectly solving corresponding structural errors of 8 th, 14 th, 17 th and 20 th columns in a matrix T through actual measurement, namely through the change of the position of the designated point of each locator moving pair in the z-direction movement posture adjustment process of a laser tracker measuring bracket; the structural error corresponding to the 9 th column in the matrix T is wound by the bracket S1S4Rotating, and indirectly calculating the space position change of a specified point on an x-direction moving axis of the measuring positioner 2; 2) byIn matrix T', 2 nd column and 22 nd column are linearly related, 3 rd column and 24 th column are linearly related, 4 th column and 30 th column are linearly related, 5 th column and 36 th column are linearly related, without loss of generality, taking 2 nd column and 22 nd column of any row as an example, then:
1×(x2+x22)+f(x1,x3L x36)＝Δii
wherein, DeltaiiMultiplying the integral error term coefficient in the process of adjusting the posture of the bracket at a time by an error term (T)pθ·δpθ)iMiddle row), f (x)1,x3L x36) To remove structural errors x2、x22Then, the remaining structural error pairs ΔiiThe influence of (a); the structural error items corresponding to the linear correlation columns cannot be identified independently, and only the comprehensive influence of the structural error items on the integral error items of the bracket can be identified; similarly, the following is solved as a single whole: x is the number of3+x24；x4+x30；x5+x36(ii) a Therefore, let:
Q2＝x2+x22；Q3＝x3+x24；Q4＝x4+x30；Q5＝x5+x36
the corresponding coefficient matrix T 'is sorted to obtain an error transformation matrix T' with the row number of 32, so that the structural error parameters needing to be identified are transformed into x1、Q2、Q3、Q4、Q5、x6、x7、x8、x9、x10、x11、x12、x13、x14、x15、x16、x17、x18、x19、x20、x21、x23、x25、x26、x27、x28、x29、x31、x32、x33、x34、x35Then the above formula is modified as follows:
T”·δ＝M
the T matrix in the above formula is subjected to dimension reduction treatment, and the strips of the matrix T are subjected to dimension reduction treatmentNumber of pieces is 1021Reduced to 10 orders of magnitude3The order of magnitude reduces the sensitivity of the matrix T to measurement errors.
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| CN110456827B (en) * | 2019-07-31 | 2022-09-27 | 南京理工大学 | Large-sized workpiece packaging box digital butt joint system and method |
| CN110849267B (en) * | 2019-12-02 | 2021-02-26 | 南京航空航天大学 | Method for positioning and converting coordinate system on product by mobile automatic system based on local reference hole |
| CN112298600B (en) * | 2020-09-18 | 2022-05-06 | 成都飞机工业（集团）有限责任公司 | Multi-axis full-active attitude adjusting method and device for large airplane component with rotating center of gravity |
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